Department of Mathematics

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Past talks for Fall 2010

October 4, 2010
Speaker: Andrejs Treibergs, Department of Mathematics University of Utah
Title: Elastic Rings and Nanotubes
Abstract: This is joint work with Feng Liu, Department of Materials Science and Engineering. Engineers are interested in the deformation of carbon nanotubes under hydrostatic pressure. A cross section of the tube can be modeled as an elastic ring, which is a classical geometric variational problem from mechanics. I'll describe the variational problem and deduce the modulus of compression.

October 18, 2010
Speaker: Grzegorz Dzierzanowski , Faculty of Civil Engineering, Warsaw Technical University
Title: Bounds on the effective isotropic moduli of thin elastic composite plates
Abstract: The main aim of the research is to estimate the effective moduli of an isotropic elastic composite analyzed within the framework of the Kirchhoff-Love theory of thin plates in bending. Results of calculations provide explicit functional correlations between homogenized properties of a composite plate made of two isotropic materials thus yielding more restrictive bounds on pairs of effective moduli than the classical (uncoupled) Hashin-Shtrikman-Walpole ones. Applying the static-geometric analogy of Lurie and Goldenveizer enables rewriting these new bounds in the two-dimensional elasticity (plane stress) setting thus revealing a link to the formulae previously found by Gibiansky and Cherkaev. Consequently, simple cross-property estimates are proposed for the plate subject to the simultaneous bending and in-plane loads.

December 10, 2010
Speaker: Kui Ren, Department of Mathematics University of Texas at Austin
Title: Quantitative photoacoustic imaging of multiple coeffcients with multiwavelength data
Abstract: The objective of quantitative photoacoustic tomography (qPAT) is the reconstruct various physical parameters of tissues from interior data on absorbed radiation. We generalize the results of Bal and Uhlmann (Bal & Uhlmann, Inverse Problems, 2010) to the problem of reconstructing simultaneously the Gruneisen, absorption and diffusion coefficients using data collected from illuminations of different wavelengths. We prove uniqueness and stability of the inverse problem. Numerical simulations based on a non-iterative procedure will be presented. Part of the talk is based on joint work with Guillaume Bal.

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